Erdos Space and Homeomorphism Groups of Manifolds
Seiten
2010
American Mathematical Society (Verlag)
978-0-8218-4635-3 (ISBN)
American Mathematical Society (Verlag)
978-0-8218-4635-3 (ISBN)
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Presents a complete solution to the topological classification problem for /mathcal{H}(M,D) as follows. If M is a one-dimensional topological manifold, then the authors proved in an earlier paper that /mathcal{H}(M,D) is homeomorphic to /mathbb{Q}^/omega, the countable power of the space of rational numbers.
Let M be either a topological manifold, a Hilbert cube manifold, or a Menger manifold and let D be an arbitrary countable dense subset of M. Consider the topological group /mathcal{H}(M,D) which consists of all autohomeomorphisms of M that map D onto itself equipped with the compact-open topology. The authors present a complete solution to the topological classification problem for /mathcal{H}(M,D) as follows. If M is a one-dimensional topological manifold, then they proved in an earlier paper that /mathcal{H}(M,D) is homeomorphic to /mathbb{Q}^/omega, the countable power of the space of rational numbers. In all other cases they find in this paper that /mathcal{H}(M,D) is homeomorphic to the famed Erdős space /mathfrak E, which consists of the vectors in Hilbert space /ell^2 with rational coordinates. They obtain the second result by developing topological characterizations of Erdős space.
Let M be either a topological manifold, a Hilbert cube manifold, or a Menger manifold and let D be an arbitrary countable dense subset of M. Consider the topological group /mathcal{H}(M,D) which consists of all autohomeomorphisms of M that map D onto itself equipped with the compact-open topology. The authors present a complete solution to the topological classification problem for /mathcal{H}(M,D) as follows. If M is a one-dimensional topological manifold, then they proved in an earlier paper that /mathcal{H}(M,D) is homeomorphic to /mathbb{Q}^/omega, the countable power of the space of rational numbers. In all other cases they find in this paper that /mathcal{H}(M,D) is homeomorphic to the famed Erdős space /mathfrak E, which consists of the vectors in Hilbert space /ell^2 with rational coordinates. They obtain the second result by developing topological characterizations of Erdős space.
| Erscheint lt. Verlag | 30.11.2010 |
|---|---|
| Reihe/Serie | Memoirs of the American Mathematical Society |
| Verlagsort | Providence |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 0-8218-4635-3 / 0821846353 |
| ISBN-13 | 978-0-8218-4635-3 / 9780821846353 |
| Zustand | Neuware |
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